Next, we integrate the proposed graph attention based convolution into an RNN. Here, we use a Gated Recurrent Unit (GRU) [1]} as an RNN unit to illustrate the integration,
where the matrix multiplications in classic GRU are replaced by the graph attention based diffusion convolutional process as defined in Equation REF .
\(r_{t} &= \sigma (\mathbf {\Theta }_r \otimes [\mathbf {X}_t|| \mathbf {H}_{t-1}] + b_r) \\u_{t} &= \sigma (\mathbf {\Theta }_u \otimes [\mathbf {X}_t|| \mathbf {H}_{t-1}] + b_u) \\\hat{h}_{t} &= tanh(\mathbf {\Theta }_{\hat{h}} \otimes [\mathbf {X}_t||(r_{t} \odot \mathbf {H}_{t-1})] + b_{\hat{h}})\\\mathbf {H}_{t} &= u_{t} \odot \mathbf {H}_{t-1} + (1-u_{t}) \odot \hat{h}_{t}\) 
